CN113011475B - Distributed fusion method considering correlated noise and random parameter matrix - Google Patents

Distributed fusion method considering correlated noise and random parameter matrix Download PDF

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CN113011475B
CN113011475B CN202110240455.0A CN202110240455A CN113011475B CN 113011475 B CN113011475 B CN 113011475B CN 202110240455 A CN202110240455 A CN 202110240455A CN 113011475 B CN113011475 B CN 113011475B
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陈宝文
程东升
李欣
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Shenzhen Institute of Information Technology
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Abstract

The invention discloses a distributed fusion algorithm considering correlated noise and a random parameter matrix, which comprises the following steps: establishing a system model doped with relevant noise and a random parameter matrix; designing a local predictor, and solving a one-step prediction mean value and covariance of a local filter; designing a local filter by using a local predictor and innovation; and correcting the predicted value of the distributed fusion predictor based on the estimation result of the local filter, and calculating the corrected mean value and covariance. The distributed fusion algorithm considering the correlated noise and the random parameter matrix is suitable for a multi-sensor nonlinear system, and based on correction of prior information of a data processing center, a distributed fusion predictor and a distributed filter are deduced.

Description

Distributed fusion method considering correlated noise and random parameter matrix
Technical Field
The invention belongs to the field of nonlinear system estimation, and particularly relates to a distributed fusion method considering correlated noise and a random parameter matrix.
Background
At present, a multi-sensor system can enhance the robustness of the system and improve the estimation accuracy of the system, so that the multi-sensor system is widely applied to target tracking and positioning, intelligent sensing, pattern recognition and the like, and a large amount of data processing methods are generated along with the multi-sensor system. The data processing method of the multi-sensor can be roughly divided into a centralized type, a distributed type and a sequential type, and the distributed fusion has the advantages of flexible structure, easiness in fault isolation and small calculation amount, so that the method is widely concerned.
For example, the patent application number is CN109543143A, the application name is a multi-sensor fusion estimation method of a nonlinear band offset system, and the fusion estimation method does not consider related noise and a random parameter matrix, so that the estimation information calculation result has the problems of inaccuracy and low precision.
Therefore, the prior art is to be improved.
Disclosure of Invention
The main objective of the present invention is to provide a distributed fusion method considering correlated noise and random parameter matrix to solve the technical problems mentioned in the background art.
The invention relates to a distributed fusion method considering correlated noise and a random parameter matrix, which comprises the following steps:
s10, establishing a system model doped with relevant noise and a random parameter matrix;
step S20, designing a local predictor, and solving a one-step prediction mean value and covariance of a local filter;
s30, designing a distributed fusion predictor according to the one-step prediction mean value and the covariance;
step S40, calculating the innovation of a local filter and a corresponding covariance matrix;
s50, designing a local filter by using a local predictor and innovation;
and S60, correcting the predicted value of the distributed fusion predictor based on the estimation result of the local filter, and calculating the corrected mean value and covariance.
Preferably, the correlated noise comprises system noise and measurement noise.
Preferably, the first and second electrodes are formed of a metal, the system model is a nonlinear system model.
Preferably, the number of sensors in the system model is at least two and the number of local predictors is at least two.
Preferably, the method further comprises the steps of:
and step S70, carrying out numerical value formatting based on a third-order sphere diameter volume rule.
Preferably, the method further comprises the steps of:
and step S80, performing simulation.
The distributed fusion method considering the correlated noise and the random parameter matrix is suitable for a multi-sensor nonlinear system, and based on correction of prior information of a data processing center, a distributed fusion predictor and a distributed filter are deduced.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the description below are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic topological diagram of a distributed fusion method of the present invention;
FIG. 2 is a diagram illustrating state estimation errors of the fusion method of the present invention and the fusion method of the patent documents mentioned in the background;
FIG. 3 is a diagram illustrating the state estimation root mean square error of the fusion method of the present invention and the fusion method of the patent documents mentioned in the background art;
fig. 4 is a schematic flow chart of a distributed fusion method considering correlated noise and a random parameter matrix according to the present invention.
The implementation, functional features and advantages of the present invention will be further described with reference to the accompanying drawings.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
It is noted that relative terms such as "first," "second," and the like may be used to describe various components, but these terms are not intended to limit the components. These terms are only used to distinguish one component from another component. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the present invention. The term "and/or" refers to a combination of any one or more of the associated items and the descriptive items.
The method of patent literature mentioned in CN109543143A in the background filed under the name of the multi-sensor fusion estimation method of nonlinear band offset system needs to calculate covariance matrix, which puts higher requirements on prior information of the system. However, the prior information often has errors, and if the prior information is not corrected, the accuracy and precision of the subsequent calculation process are easily influenced.
The invention discloses a distributed fusion method considering correlated noise and a random parameter matrix, which comprises the following steps:
s10, establishing a system model doped with relevant noise and a random parameter matrix;
in step S10, the system model is as follows:
Figure GDA0003893159990000031
Figure GDA0003893159990000032
where x is k ∈R n Is the state of the n-dimensional system,
Figure GDA0003893159990000033
is m i Dimension sensor measurement, omega k ∈R r Is r-dimensional system noise; the correlated noise comprises system noise and measurement noise;
and
Figure GDA0003893159990000034
is si-dimensional measurement noise, and
Figure GDA0003893159990000035
is a relevant random parameter matrix of a suitable dimension at time k, N is the number of sensors, the subscript i represents the ith sensor, and f and h are known nonlinear functions.
Condition 1: random parameter matrix
Figure GDA0003893159990000041
Is synchronously cross-correlated, uncorrelated with system noise and measurement noise, and satisfies
Figure GDA0003893159990000042
Here, the
Figure GDA0003893159990000043
And
Figure GDA0003893159990000044
respectively represent
Figure GDA0003893159990000045
And
Figure GDA0003893159990000046
the (i, j) and (s, u) positions of (a);
condition 2: omega k And
Figure GDA0003893159990000047
is a correlated zero mean white noise sequence and satisfies
Figure GDA0003893159990000048
Definition of
Figure GDA0003893159990000049
Is obviously provided with
Figure GDA00038931599900000410
Definition of
Figure GDA00038931599900000411
Here, the
Figure GDA00038931599900000412
And with
Figure GDA00038931599900000413
Identical in meaning, but possibly representing different matrices,
Figure GDA00038931599900000414
is represented by
Figure GDA00038931599900000415
And
Figure GDA00038931599900000416
the resulting matrix is calculated and the matrix is calculated,
Figure GDA00038931599900000417
and theta k And η k And with
Figure GDA00038931599900000418
And
Figure GDA00038931599900000419
independent.
Note: for two matrices
Figure GDA00038931599900000420
And
Figure GDA00038931599900000421
after the computation of the trace derivation, the following conclusion is generally established
Figure GDA00038931599900000422
Figure GDA00038931599900000423
Reconstructing process noise and measurement noise into
Figure GDA00038931599900000424
Figure GDA00038931599900000425
Then systems (1) and (2) can be rewritten as
Figure GDA00038931599900000426
Figure GDA00038931599900000427
And the reconstructed noise has the following relation:
Figure GDA0003893159990000051
step S20, designing a local predictor, and solving a one-step prediction mean value and covariance of a local filter; (related to formula 8-24)
The embodiment of the present invention is described by taking two sensors as an example, and can be actually applied to a multi-sensor nonlinear system, as shown in fig. 1;
introduction 1: local predictor design:
Figure GDA0003893159990000052
Figure GDA0003893159990000053
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003893159990000054
here, the number of the first and second electrodes,
Figure GDA0003893159990000055
representing the space spanned by the elements in L,
Figure GDA0003893159990000056
Figure GDA0003893159990000057
wherein the content of the first and second substances,
Figure GDA0003893159990000058
according to the definition of the error, have
Figure GDA0003893159990000061
Considering that the three terms in the above formula brackets are not related to each other, then
Figure GDA0003893159990000062
Wherein
Figure GDA0003893159990000063
Is an intermediate variable, taking the value of
Figure GDA0003893159990000064
Figure GDA0003893159990000065
Figure GDA0003893159990000071
Here, the
Figure GDA0003893159990000072
Figure GDA0003893159990000073
Figure GDA0003893159990000074
Figure GDA0003893159990000075
Figure GDA0003893159990000076
Figure GDA0003893159990000081
Figure GDA0003893159990000082
Figure GDA0003893159990000083
Wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003893159990000084
here, E [ g ] 1 (g 2 ) T |η 1 ，η 2 ]Is represented by g 1 In eta 1 Calculated under the conditions of g 2 In eta 2 Calculated under the conditions, and g 1 And g 2 Representing two non-linear functions, η 1 And η 2 Indicating that measurements have been obtained. For the ith predictor, its initial value is taken as
Figure GDA0003893159990000085
Will be provided with
Figure GDA0003893159990000086
The local filter one-step prediction cross covariance matrix can be obtained by substituting (13), and the one-step prediction mean values can be obtained by substituting (10), (11) into (8) and (9).
Correcting the prior information of the data processing center by using local prediction information to enable X k+1 ＝ex k+1 Then, then
Figure GDA0003893159990000087
Figure GDA0003893159990000088
Wherein
Figure GDA0003893159990000089
S30, designing a distributed fusion predictor according to the one-step prediction mean value and the covariance; the method comprises the following specific steps:
theorem 1: for systems (5) and (6), under the condition that the assumptions 1 and 2 are satisfied, the distributed optimal fusion predictor is designed as follows:
Figure GDA0003893159990000091
CN109543143A, which is referred to in the background art, is a multi-sensor fusion estimation method of a nonlinear band offset system, and the method in the above patent literature needs to calculate a covariance matrix, which puts higher requirements on prior information of the system. However, the prior information often has errors, and if the prior information is not corrected, the accuracy and precision of the subsequent calculation process are easily affected.
In the patent documents mentioned in the background art mentioned above; for distributed optimal fusion predictor design, unlike the present application.
The difference points are that: the distributed fusion predictor corrects the prior information of the data center based on the local prediction information.
Thus: compared with the method that the conclusion under a linear system is popularized based on an EKF algorithm, the distributed fusion predictor and the distributed filter are deduced, and higher estimation accuracy can be obtained when a corresponding estimator is designed for the nonlinear system to process the nonlinear problem.
L k+1 Given in the course of the certification process.
And (3) proving that:
Figure GDA0003893159990000101
the local prediction error of arrangement is
Figure GDA0003893159990000102
Wherein the content of the first and second substances,
Figure GDA0003893159990000103
Figure GDA0003893159990000104
Figure GDA0003893159990000105
Figure GDA0003893159990000106
the one-step prediction error covariance matrix is
Figure GDA0003893159990000107
Wherein the content of the first and second substances,
Figure GDA0003893159990000108
means all of
Figure GDA0003893159990000109
And the matrix is arranged in the order of i rows and j columns.
Figure GDA0003893159990000111
It is worth mentioning that according to the definitions of the matrices A, B in equations (46) - (47), Λ can be rewritten as
Figure GDA0003893159990000112
Here, the
Figure GDA0003893159990000113
E[f(x k )f T (x k )]＝∫f(x k )f T (x k )N 3 dx k (36)
Figure GDA0003893159990000114
Figure GDA0003893159990000115
Figure GDA0003893159990000116
E[f(x k )h T (x k )]＝∫f(x k )h T (x k )N 4 dx k (40)
Figure GDA0003893159990000117
Wherein
Figure GDA0003893159990000118
Based on the minimum mean square error criterion, L k+1 Find out as follows
Figure GDA0003893159990000121
Wherein
Figure GDA0003893159990000122
For the derivation operator, H and M represent the derived primary term and the constant term, respectively. For the sake of clarity, to
Figure GDA0003893159990000123
The derivation process is divided into three parts including lambda part derivation and lambda T The partial derivation and the rest derivation corresponding to the first order term and the constant term are respectively represented as H 1 ，H 2 ，H 3 ，M 1 ，M 2 ，M 3 The concrete arrangement is as follows
Figure GDA0003893159990000124
In view of
Figure GDA0003893159990000125
Thus, it is possible to provide
H 2 ＝H 1 (44)
Figure GDA0003893159990000126
Wherein
Figure GDA0003893159990000127
Figure GDA0003893159990000128
Figure GDA0003893159990000129
Figure GDA00038931599900001210
Then there is
Figure GDA0003893159990000131
Figure GDA0003893159990000132
In view of
Figure GDA0003893159990000133
Then
M 2 ＝M 1 (52)
Figure GDA0003893159990000134
Then there is
Figure GDA0003893159990000135
Thus, the device
Figure GDA0003893159990000136
Mixing L with k+1 And the values of A and B are substituted into (33) to obtain Λ, and L is k+1 And lambda is substituted into (32) to obtain a one-step predicted covariance, L k+1 Carry in (25) toOne step prediction mean value
S40, calculating the innovation of a local filter and a corresponding covariance matrix; the method comprises the following specific steps:
2, leading: for systems (5) and (6), the innovation and its covariance are calculated as follows:
Figure GDA0003893159990000141
wherein the content of the first and second substances,
Figure GDA0003893159990000142
for the sake of simplicity, rewriting
Figure GDA0003893159990000143
Is composed of
Figure GDA0003893159990000144
Then the
Figure GDA0003893159990000145
The innovation cross-covariance of
Figure GDA0003893159990000146
S50, designing a local filter by using a local predictor and innovation; the method comprises the following specific steps:
and 3, introduction: for systems (5) and (6), the local filter design is as follows:
Figure GDA0003893159990000151
Figure GDA0003893159990000152
wherein the content of the first and second substances,
Figure GDA0003893159990000153
the state covariance is calculated as follows:
Figure GDA0003893159990000154
in view of
Figure GDA0003893159990000155
Then there is
Figure GDA0003893159990000156
Taken into the covariance matrix to obtain
Figure GDA0003893159990000157
The cross covariance matrix is calculated as follows
Figure GDA0003893159990000158
Wherein
Figure GDA0003893159990000161
Figure GDA0003893159990000162
Solving process and
Figure GDA0003893159990000163
similarly, no further description is given.
S60, correcting the predicted value of the distributed fusion predictor based on the estimation result of the local filter, and calculating the corrected mean value and covariance; the method comprises the following specific steps:
theorem 2: for systems (5) and (6), the measurement update mean is calculated as follows:
Figure GDA0003893159990000164
wherein L is k+1 Given in the course of the certification process.
And (3) proving that:
Figure GDA0003893159990000165
local measurement error is rewritten as
Figure GDA0003893159990000166
The local prediction error of the arrangement is
Figure GDA0003893159990000171
Like
Figure GDA0003893159990000172
Here, the
Figure GDA0003893159990000173
The measurement update error covariance matrix is
Figure GDA0003893159990000174
Based on the minimum mean square error criterion, have
Figure GDA0003893159990000175
The simple algebraic operation of the formula (74) includes
Figure GDA0003893159990000176
Wherein
Figure GDA0003893159990000177
Here, the first and second liquid crystal display panels are,
Figure GDA0003893159990000181
and is
Figure GDA0003893159990000182
Wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003893159990000183
by
Figure GDA0003893159990000184
The definition of the compound can be known,
Figure GDA0003893159990000185
it is obvious that
Figure GDA0003893159990000186
The information in (1) has been calculated in a one-step prediction process, so that equation (76) can be derived, substituting (76) into (75) the available L k+1 From (75) and L k+1 The corrected covariance is obtained by substituting (73) L k+1 The corrected estimate is available (69).
Aiming at a nonlinear multi-sensor system with a random parameter matrix and related noise, the invention corrects prior information of a data processing center by taking a local estimation state as measurement and transmitting the measurement to the data processing center, and deduces a distributed fusion predictor and a distributed filter.
Specific numerical implementation forms are as follows; local predictor design:
let us assume that the k-1 time information is known
Figure GDA0003893159990000187
1) Decomposition of
Figure GDA0003893159990000191
Figure GDA0003893159990000192
2) Calculating volume points
Figure GDA0003893159990000193
Figure GDA0003893159990000194
3) Volumetric point propagation
Figure GDA0003893159990000195
Figure GDA0003893159990000196
Figure GDA0003893159990000197
Figure GDA0003893159990000198
Figure GDA0003893159990000199
4) Local prediction mean and covariance calculation
Figure GDA00038931599900001910
Figure GDA00038931599900001911
Figure GDA00038931599900001912
Figure GDA0003893159990000201
Figure GDA0003893159990000202
Figure GDA0003893159990000203
The mean and gain matrix of the local filter can be obtained by substituting the equations (87) and (88) into (8) and (9), and the cross covariance matrix of the local filter can be obtained by substituting the equations (89) - (91) into (13).
Designing a distributed fusion predictor:
let us assume that the k-1 time information is known
Figure GDA0003893159990000204
1) Decomposition of
Figure GDA0003893159990000205
Figure GDA0003893159990000206
2) Calculating volume points
Figure GDA0003893159990000207
Figure GDA0003893159990000208
3) Volumetric point propagation
Figure GDA0003893159990000211
Figure GDA0003893159990000212
Figure GDA0003893159990000213
Figure GDA0003893159990000214
Figure GDA0003893159990000215
4) Fused mean and covariance calculation
Figure GDA0003893159990000216
Figure GDA0003893159990000217
Figure GDA0003893159990000218
Figure GDA0003893159990000219
Figure GDA0003893159990000221
Substituting the values of A, B and C into Λ and L k+1 The predicted mean and covariance are obtained.
And (3) innovation calculation:
assuming that the one-step prediction information at time k is known, let
Figure GDA0003893159990000222
1) Decomposition of
Figure GDA0003893159990000223
Figure GDA0003893159990000224
2) Calculating volume points
Figure GDA0003893159990000225
Figure GDA0003893159990000226
3) Volumetric point propagation
Figure GDA0003893159990000227
Figure GDA0003893159990000228
Figure GDA0003893159990000229
4) Innovation and covariance calculation
Figure GDA00038931599900002210
Figure GDA00038931599900002211
The innovation cross-covariance of
Figure GDA0003893159990000231
Local filter design:
Figure GDA0003893159990000232
1) Decomposition of
Figure GDA0003893159990000233
Figure GDA0003893159990000234
2) Calculating volume points
Figure GDA0003893159990000235
Figure GDA0003893159990000236
3) Volumetric point propagation
Figure GDA0003893159990000237
Figure GDA0003893159990000238
4) Covariance calculation
Figure GDA0003893159990000239
Figure GDA00038931599900002310
The local filter mean and covariance are obtained by substituting them.
Designing a fusion filter:
Figure GDA0003893159990000241
Figure GDA0003893159990000242
1) Decomposition of
Figure GDA0003893159990000243
Figure GDA0003893159990000244
2) Calculating volume points
Figure GDA0003893159990000245
Figure GDA0003893159990000246
3) Volumetric point propagation
Figure GDA0003893159990000247
Figure GDA0003893159990000248
Figure GDA0003893159990000249
Figure GDA00038931599900002410
4) Covariance calculation
Figure GDA00038931599900002411
Figure GDA0003893159990000251
The above equations 78-139; the numerical value given realizes the format based on the third-order sphere diameter volume rule for the convenience of computer simulation.
The simulation process is as follows:
to verify the validity of the proposed algorithm, a strong non-linear model is given as follows
Figure GDA0003893159990000252
Figure GDA0003893159990000253
Figure GDA0003893159990000254
Φ k ＝I 3×3 +ξ k diag([0.01 0.01 0.01]) (143)
Figure GDA0003893159990000255
Figure GDA0003893159990000256
Figure GDA0003893159990000257
Figure GDA0003893159990000261
Figure GDA0003893159990000262
Wherein omega k ，η k ，ξ k ，γ k Is uncorrelated white Gaussian noise, and has covariance of 1,0.5,0.1,0.3 and initial state value of x 0 ＝[-0.7 1 1] T The filter initial value is taken as
Figure GDA0003893159990000263
30 independent monte carlo simulations are performed, and the corresponding simulation results are shown in fig. 2 and fig. 3.
When the method is popularized to a nonlinear system based on the EKF to process the nonlinear estimation problem, smaller estimation error and root mean square error can be obtained, which shows that under the nonlinear system, compared with the method for popularizing the conclusion under the linear system based on the EKF, the method directly designs a nonlinear filter aiming at the conclusion under the linear system, and higher estimation precision can be obtained.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all equivalent structures or equivalent processes performed by the present invention or directly or indirectly applied to other related technical fields are also included in the scope of the present invention.

Claims (4)

1. A distributed fusion method considering correlated noise and a random parameter matrix is characterized by comprising the following steps:
s10, establishing a system model doped with relevant noise and a random parameter matrix; the system model is as follows:
Figure FDA0003893159980000011
Figure FDA0003893159980000012
where x is k ∈R n Is the state of the n-dimensional system,
Figure FDA0003893159980000013
is m i Dimension sensor measurement, omega k ∈R r Is r-dimensional system noise, the correlated noise includes system noise and measurement noise, an
Figure FDA0003893159980000014
Is s i Measure the noise in dimension, and
Figure FDA0003893159980000015
the method comprises the following steps that a relevant random parameter matrix with proper dimensionality at the moment k is obtained, N is the number of sensors, an angle mark i represents the ith sensor, and f and h are known nonlinear functions;
condition 1: random parameter matrix
Figure FDA0003893159980000016
Is synchronously cross-correlated, uncorrelated with system noise and measurement noise, and satisfies
Figure FDA0003893159980000017
Here, the
Figure FDA0003893159980000018
And
Figure FDA0003893159980000019
respectively represent
Figure FDA00038931599800000110
And
Figure FDA00038931599800000111
the (i, j) and (s, u) positions of (a);
condition 2: omega k And
Figure FDA00038931599800000112
is a correlated zero mean white noise sequence and satisfies
Figure FDA0003893159980000021
Definition of
Figure FDA0003893159980000022
Is obviously provided with
Figure FDA0003893159980000023
Definition of
Figure FDA0003893159980000024
Here, the
Figure FDA0003893159980000025
And
Figure FDA0003893159980000026
are identical in meaning, but represent different matrices,
Figure FDA0003893159980000027
is represented by
Figure FDA0003893159980000028
And
Figure FDA0003893159980000029
the resulting matrix is calculated and the matrix is calculated,
Figure FDA00038931599800000210
and theta k And η k And
Figure FDA00038931599800000211
and
Figure FDA00038931599800000212
is independent;
for theTwo matrices
Figure FDA00038931599800000213
And
Figure FDA00038931599800000214
after the computation of the trace derivation, the following conclusion is generally established
Figure FDA00038931599800000215
Figure FDA00038931599800000216
Reconstructing process noise and measurement noise into
Figure FDA00038931599800000217
i =1, …, N, then systems (1) and (2) may be rewriteable as
Figure FDA00038931599800000218
Figure FDA00038931599800000219
And the reconstructed noise has the following relation:
Figure FDA00038931599800000220
s20, designing a local predictor, and solving a one-step prediction mean value and covariance of a local filter; a nonlinear system for realizing multiple sensors;
local predictor design:
Figure FDA0003893159980000031
Figure FDA0003893159980000032
wherein the content of the first and second substances,
Figure FDA0003893159980000033
here, the first and second liquid crystal display panels are,
Figure FDA0003893159980000034
representing the space spanned by the elements in L,
Figure FDA0003893159980000035
Figure FDA0003893159980000036
wherein the content of the first and second substances,
Figure FDA0003893159980000037
according to the definition of error, there are
Figure FDA0003893159980000041
Considering that the three terms in the above formula are not related to each other, then
Figure FDA0003893159980000042
Wherein
Figure FDA0003893159980000043
Figure FDA0003893159980000044
Figure FDA0003893159980000045
Here, the
Figure FDA0003893159980000051
Figure FDA0003893159980000052
Figure FDA0003893159980000053
Figure FDA0003893159980000054
Figure FDA0003893159980000055
Figure FDA0003893159980000056
Figure FDA0003893159980000057
Figure FDA0003893159980000058
Wherein the content of the first and second substances,
Figure FDA0003893159980000059
here, the first and second liquid crystal display panels are,
Figure FDA00038931599800000510
denotes g 1 In eta 1 Under the condition of calculating, g 2 In eta 2 Calculated under the conditions, and g 1 And g 2 Representing two non-linear functions, η 1 And η 2 Indicating that measurements have been obtained; for the ith predictor, its initial value is taken as
Figure FDA0003893159980000061
Will make Ψ 1 ，Ψ 2 ，Ψ 3 The local filter one-step prediction cross covariance matrix can be obtained by substituting (13), and the one-step prediction mean values can be obtained by substituting (10) and (11) into (8) and (9);
correcting the prior information of the data processing center by using local prediction information to enable X k+1 ＝ex k+1 Then, then
Figure FDA0003893159980000062
S30, designing a distributed fusion predictor according to the one-step prediction mean value and the covariance; the method comprises the following specific steps:
for systems (5) and (6), under the conditions satisfied by conditions 1 and 2, the distributed optimal fusion predictor is designed as follows:
Figure FDA0003893159980000063
step S40, calculating the innovation of a local filter and a corresponding covariance matrix; the method comprises the following specific steps:
for systems (5) and (6), the innovation and its covariance are calculated as follows:
Figure FDA0003893159980000064
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003893159980000065
for the sake of simplicity, rewriting
Figure FDA0003893159980000071
Is composed of
Figure FDA0003893159980000072
Then
Figure FDA0003893159980000073
The innovation cross-covariance of
Figure FDA0003893159980000074
S50, designing a local filter by using a local predictor and innovation; the method comprises the following specific steps:
Figure FDA0003893159980000075
Figure FDA0003893159980000081
wherein the content of the first and second substances,
Figure FDA0003893159980000082
the state covariance is calculated as follows:
Figure FDA0003893159980000083
in view of
Figure FDA0003893159980000084
Then there is
Figure FDA0003893159980000085
Taken into the covariance matrix to obtain
Figure FDA0003893159980000086
The cross covariance matrix is calculated as follows
Figure FDA0003893159980000087
Wherein
Figure FDA0003893159980000091
Figure FDA0003893159980000092
Solving process and
Figure FDA0003893159980000095
the same;
s60, correcting the predicted value of the distributed fusion predictor based on the estimation result of the local filter, and calculating the mean value and covariance after correction; the method comprises the following specific steps:
for systems (5) and (6), the measurement update mean is calculated as follows:
Figure FDA0003893159980000093
wherein L is k+1 Given in the course of certification
And (3) proving that:
Figure FDA0003893159980000094
local measurement error is rewritten as
Figure FDA0003893159980000101
The local prediction error of arrangement is
Figure FDA0003893159980000102
Like
Figure FDA0003893159980000103
Here, the
Figure FDA0003893159980000104
The measurement update error covariance matrix is
Figure FDA0003893159980000105
Based on the minimum mean square error criterion, have
Figure FDA0003893159980000106
Then there is
Figure FDA0003893159980000107
Wherein
Figure FDA0003893159980000111
Here, the first and second liquid crystal display panels are,
Figure FDA0003893159980000112
and is
Figure FDA0003893159980000113
Wherein the content of the first and second substances,
Figure FDA0003893159980000114
by
Figure FDA0003893159980000115
The definition of the compound can be known,
Figure FDA0003893159980000116
it is obvious that
Figure FDA0003893159980000117
The information in (1) is calculated in a one-step prediction process, so that the formula (76) is obtained, and the formula (76) is substituted into the formula (75) to obtain L k+1 Mixing (75) with L k+1 The corrected covariance is obtained by substituting (73) L k+1 The corrected estimate is available (69).
2. The method of claim 1, wherein the number of sensors in the system model is at least two and the number of local predictors is at least two.
3. The distributed fusion method of claim 1 taking into account correlated noise and a random parameter matrix, further comprising the steps of:
and step S70, carrying out numerical value formatting based on a third-order sphere diameter volume rule.
4. The distributed fusion method taking into account correlated noise and a random parameter matrix according to claim 1, further comprising the steps of:
and step S80, performing simulation.
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104035067A (en) * 2014-06-13 2014-09-10 重庆大学 Mobile robot automatic positioning algorithm based on wireless sensor network
CN106291533A (en) * 2016-07-27 2017-01-04 电子科技大学 A kind of distributed multi-sensor blending algorithm based on AMD
CN107994885A (en) * 2017-11-21 2018-05-04 郑州鼎创智能科技有限公司 Distributed fused filtering method that is a kind of while estimating Unknown worm and state
CN109543143A (en) * 2019-01-28 2019-03-29 杭州电子科技大学 The Multi-sensor Fusion estimation method of non-linear belt bias system
CN111735458A (en) * 2020-08-04 2020-10-02 西南石油大学 Navigation and positioning method of petrochemical inspection robot based on GPS, 5G and vision
CN111985093A (en) * 2020-08-03 2020-11-24 哈尔滨工程大学 Adaptive unscented Kalman filtering state estimation method with noise estimator

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108536171B (en) * 2018-03-21 2020-12-29 电子科技大学 Path planning method for collaborative tracking of multiple unmanned aerial vehicles under multiple constraints
CN110262334B (en) * 2019-06-17 2021-05-28 江南大学 Finite time domain H-infinity control method of state saturation system under random communication protocol
CN111193528B (en) * 2019-12-30 2021-09-17 哈尔滨工业大学 Gaussian filtering method based on non-linear network system under non-ideal condition

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104035067A (en) * 2014-06-13 2014-09-10 重庆大学 Mobile robot automatic positioning algorithm based on wireless sensor network
CN106291533A (en) * 2016-07-27 2017-01-04 电子科技大学 A kind of distributed multi-sensor blending algorithm based on AMD
CN107994885A (en) * 2017-11-21 2018-05-04 郑州鼎创智能科技有限公司 Distributed fused filtering method that is a kind of while estimating Unknown worm and state
CN109543143A (en) * 2019-01-28 2019-03-29 杭州电子科技大学 The Multi-sensor Fusion estimation method of non-linear belt bias system
CN111985093A (en) * 2020-08-03 2020-11-24 哈尔滨工程大学 Adaptive unscented Kalman filtering state estimation method with noise estimator
CN111735458A (en) * 2020-08-04 2020-10-02 西南石油大学 Navigation and positioning method of petrochemical inspection robot based on GPS, 5G and vision

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